Bernoulli

  • Bernoulli
  • Volume 23, Number 4A (2017), 2917-2950.

Guided proposals for simulating multi-dimensional diffusion bridges

Moritz Schauer, Frank van der Meulen, and Harry van Zanten

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Abstract

A Monte Carlo method for simulating a multi-dimensional diffusion process conditioned on hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges are obtained by superimposing an additional guiding term to the drift of the process under consideration. The guiding term is derived via approximation of the target process by a simpler diffusion processes with known transition densities. Acceptance of a proposal can be determined by computing the likelihood ratio between the proposal and the target bridge, which is derived in closed form. We show under general conditions that the likelihood ratio is well defined and show that a class of proposals with guiding term obtained from linear approximations fall under these conditions.

Article information

Source
Bernoulli, Volume 23, Number 4A (2017), 2917-2950.

Dates
Received: September 2014
Revised: October 2015
First available in Project Euclid: 9 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1494316837

Digital Object Identifier
doi:10.3150/16-BEJ833

Mathematical Reviews number (MathSciNet)
MR3648050

Zentralblatt MATH identifier
06778261

Keywords
change of measure data augmentation linear processes multidimensional diffusion bridge

Citation

Schauer, Moritz; van der Meulen, Frank; van Zanten, Harry. Guided proposals for simulating multi-dimensional diffusion bridges. Bernoulli 23 (2017), no. 4A, 2917--2950. doi:10.3150/16-BEJ833. https://projecteuclid.org/euclid.bj/1494316837


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